Transient dynamics and early diagnostics in infectious disease

Abstract.

To date, mathematical models of the dynamics of infectious disease have consistently focused on understanding the long-term behavior of the interacting components, where the steady state solutions are paramount. However for most acute infections, the long-term behavior of the pathogen population is of little importance to the host and population health. We introduce the notion of transient pathology, where the short-term dynamics of interaction between the immune system and pathogens is the principal focus. We identify the amplifying effect of the absence of a fully operative immune system on the pathogenesis of the initial inoculum, and its implication for the acute severity of the infection. We then formalize the underlying dynamics, and derive two measures of transient pathogenicity: the peak of infection (maximum pathogenic load) and the time to peak of infection, both crucial to understanding the early dynamics of infection and its consequences for early intervention.